Molecular mass dependence of point-to-set correlation length scale in polymers

We use a recently proposed metric, termed the point-to-set correlation functions, to probe the molecular weight dependence of the relevant static length scales in glass-forming oligomeric chain liquids of 4, 5, 8, and 10 repeat units. In agreement with the results for simple, monatomic fluids, we find that static length scales of the oligomers increase monotonically when the temperature is lowered towards the glass transition temperature of the fluid. More interestingly, the static length scale increases with increasing chain length. Within the bounds of error in our simulations, the static length scale appears to scale as the radius of gyration of the oligomer, but with a prefactor, which is much larger than unity and which grows with the temperature. The preceding behavior contrasts with the length scales extracted from the radial distribution function of the oligomer system, which is practically independent of the chain length.